Gọi G là trọng tâm tam giác MNP, em vẽ hình vào bài nhé em:
\(\begin{array}{l}
\Rightarrow \overrightarrow {GM} + \overrightarrow {GN} + \overrightarrow {GP} = \overrightarrow 0 \\
\Leftrightarrow \overrightarrow {MG} + \overrightarrow {NG} + \overrightarrow {PG} = \overrightarrow 0 \\
a)\,\,\,\overrightarrow {MQ} + \overrightarrow {NS} + \overrightarrow {PI} = \frac{3}{2}\overrightarrow {MG} + \frac{3}{2}\overrightarrow {NG} + \frac{3}{2}\overrightarrow {PG} \\
= \frac{3}{2}\left( {\overrightarrow {MG} + \overrightarrow {NG} + \overrightarrow {PG} } \right) = \overrightarrow 0 \,\,\,\,\left( {dpcm} \right).\\
b)\,\,\,\overrightarrow {GQ} + \overrightarrow {GS} + \overrightarrow {GI} = \frac{1}{2}\overrightarrow {MG} + \frac{1}{2}\overrightarrow {NG} + \frac{1}{2}\overrightarrow {PG} \\
= \frac{1}{2}\left( {\overrightarrow {MG} + \overrightarrow {NG} + \overrightarrow {PG} } \right) = \overrightarrow 0 \\
\Rightarrow G\,\,\,la\,\,\,trong\,\,tam\,\,\Delta SQI.
\end{array}\)
